Mathematical Sciences: Asymptotic Behavior of Brownian Motion and Random Walk Processes

数学科学：布朗运动和随机游走过程的渐近行为

• 批准号: 8807121
• 负责人: Victor Goodman
• 金额: $ 2.96万
• 依托单位: Indiana University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1988
• 资助国家: 美国
• 起止时间: 1988-07-15 至 1990-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8807121&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Asymptotic; Behavior; Brownian

The principal investigator will continue his study of the upper and lower tail behavior of vector valued Brownian motion. Results in this direction can be used for estimating the behavior of other Gaussian processes such as a two parameter Kiefer process. The oscillatory behavior of these processes is studied via the discrepancy between collections of sample paths and certain non-random set functions. The non-random set functions are metric entropy of balls in the reproducing kernel Hilbert space of the Brownian motion. Error rates for the convergence of the processes to their cluster sets and the approximate density of sample path collections is established. The research will contribute to the observable regularities within a widely-studied framework involving long-time chaos.

首席研究员将继续研究矢量值布朗运动的上尾和下尾行为。 这个方向的结果可用于估计其他高斯过程的行为，例如二参数基弗过程。 这些过程的振荡行为是通过样本路径集合与某些非随机集合函数之间的差异来研究的。 非随机集合函数是布朗运动的再现核希尔伯特空间中球的度量熵。 建立了过程收敛到其簇集的错误率和样本路径集合的近似密度。 这项研究将有助于在涉及长期混沌的广泛研究框架内发现可观察到的规律。